class Fibonacci {

    /* Recursively computes the nth fibonacci number according to definition. */
    static long rfib(int n) {
        if (n < 2)
            return n;
        return rfib(n-1) + rfib(n-2);
    }

///////////////////////////////////////////////////////////////////////////////////
    /* Computes the nth fibonacci number using bottom-up Dynamic Programming. */
    static long dpfib(int n) {
        if (n < 2)
            return n;
        long[] table = new long[n+1];
        table[0] = 0; table[1] = 1;
        for (int i = 2; i <= n; i++)
            table[i] = table[i-1] + table[i-2];
        return table[n];
    }
///////////////////////////////////////////////////////////////////////////////////

    /* Computes the nth fibonacci number using space-efficient bottom-up Dynamic Programming. */
    static long dpfib_space(int n) {
        if (n < 2) return n;
        long fn_2 = 0, fn_1 = 1;
        for (int i = 2; i <= n; i++) {
            long temp = fn_1;
            fn_1 += fn_2;
            fn_2 = temp;
        }
        return fn_1;
    }
///////////////////////////////////////////////////////////////////////////////////

    // Any value that's impossible for a fibonacci number will do.
    static final long UNKNOWN = -1;

    /* Precondition: n >= 0
     * Computes the nth fibonacci number using Memoization.
     */
    static long mpfib(int n) {
        // Creates the table and fills it with UNKNOWN.
        long[] table = new long[n+1];
        for (int i = 0; i <= n; i++)
            table[i] = UNKNOWN;
        
        // Computes f(n) using the recurrence & the table.
        return memoize(n, table);
    }

    /* Precondition: n >= 0 */
    static long memoize(int n, long[] table) {
        if (table[n] == UNKNOWN) {
            if (n < 2) {
                table[n] = n;
            } else {
                table[n] = memoize(n-1, table) + memoize(n-2, table);
            }
        }
        return table[n];
    }


    public static void main(String[] args) {

        for (int n = 0; n < 10; n++) {
            System.out.printf("rfib(%d) = %d, ", n, rfib(n));
            System.out.printf("dpfib(%d) = %d, ", n, dpfib(n));
            System.out.printf("dpfib_space(%d) = %d%n", n, dpfib_space(n));
            System.out.printf("mpfib(%d) = %d%n", n, mpfib(n));
        }

        int n = 40;
        Stopwatch watch = new Stopwatch();

 /*       
        System.out.printf("rfib(%d) = %d%n", n, rfib(n));
        double t1 = watch.elapsedTime();
        System.out.printf("time for rfib(%d) is %f%n", n, t1);

        System.out.printf("mpfib(%d) = %d%n", n, mpfib(n));
        double t1 = watch.elapsedTime();
        System.out.printf("time for mpfib(%d) is %f%n", n, t1);

        System.out.printf("dpfib(%d) = %d%n", n, dpfib(n));
        double t2 = watch.elapsedTime();
        System.out.printf("time for dpfib(%d) is %f%n", n, t2-t1);
*/

    }
}